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Tomkowicz J, Kułakowski K. Scaling of connected spin avalanches in growing networks. Phys Rev E Stat Nonlin Soft Matter Phys. 2010;81(5):052101doi: 10.1103/PhysRevE.81.052101.
Tomkowicz, J., & Kułakowski, K. (2010). Scaling of connected spin avalanches in growing networks. Physical review. E, Statistical, nonlinear, and soft matter physics, 81(5), 052101. https://doi.org/10.1103/PhysRevE.81.052101
Tomkowicz, Joanna, and Kułakowski, Krzysztof. "Scaling of connected spin avalanches in growing networks." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 81,5 (2010): 052101. doi: https://doi.org/10.1103/PhysRevE.81.052101
Tomkowicz J, Kułakowski K. Scaling of connected spin avalanches in growing networks. Phys Rev E Stat Nonlin Soft Matter Phys. 2010 May;81(5):052101. doi: 10.1103/PhysRevE.81.052101. Epub 2010 May 21. PMID: 20866281.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2010 May;81(5):052101. doi: 10.1103/PhysRevE.81.052101. Epub 2010 May 21.

Scaling of connected spin avalanches in growing networks.

Physical review. E, Statistical, nonlinear, and soft matter physics

Joanna Tomkowicz, Krzysztof Kułakowski

Affiliations

  1. Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland. [email protected]

PMID: 20866281 DOI: 10.1103/PhysRevE.81.052101

Abstract

We use the damage spreading method to investigate the spectra of connected spin avalanches in the exponential networks and the scale-free networks with antiferromagnetically coupled spins. The results suggest that the avalanche spectra are characterized by the same statistics as the degree distribution in their home networks. Further, the obtained mean range Z of an avalanche, i.e., the maximal distance reached by an avalanche from the damaged site, scales with the avalanche size s as Z/N β=f(s/N α), where α=0.5 and β=0.33. These values are true for both kinds of networks for the number M of nodes to which new nodes are attached between 4 and 10; a check for M=25 confirms these values as well.

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